On the asymptotic properties of a residential heater/air conditioner duty cycle

The asymptotic properties of two probabilistic solutions for the duty cycle of a residential thermostat controlled heater/air conditioner unit was considered. The probabilistic solutions were derived previously from a physical thermodynamical model of the indoor temperature of a residential house as seen by a thermostat. The duty cycle solutions considered are functions of the house parameters, outdoor temperature, and the random effects of household activities (driving noise process). It is shown that the conventional (deterministic) duty cycle represents, as expected, a special case of the two solutions.<
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